Solve for $x$ and $y$ using elimination. ${3x+2y = 15}$ ${4x-y = -2}$
Explanation: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the bottom equation by $2$ ${3x+2y = 15}$ $8x-2y = -4$ Add the top and bottom equations together. $11x = 11$ $\dfrac{11x}{{11}} = \dfrac{11}{{11}}$ ${x = 1}$ Now that you know ${x = 1}$ , plug it back into $\thinspace {3x+2y = 15}\thinspace$ to find $y$ ${3}{(1)}{ + 2y = 15}$ $3+2y = 15$ $3{-3} + 2y = 15{-3}$ $2y = 12$ $\dfrac{2y}{{2}} = \dfrac{12}{{2}}$ ${y = 6}$ You can also plug ${x = 1}$ into $\thinspace {4x-y = -2}\thinspace$ and get the same answer for $y$ : ${4}{(1)}{ - y = -2}$ ${y = 6}$